Finding Transition Pathways on Manifolds

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

8 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)173-206
Journal / PublicationMultiscale Modeling & Simulation
Volume14
Issue number1
Online published26 Jan 2016
Publication statusPublished - 2016

Abstract

When a randomly perturbed dynamical system is subject to some constraints, the trajectories of the system and the noise-induced most probable transition pathways are restricted on the manifold associated with the given constraints. We present a constrained minimum action method to compute the optimal transition pathways on manifolds. By formulating the constrained stochastic dynamics in a Stratonovich stochastic differential equation of the projection form, we consider the system as embedded in the Euclidean space and present the Freidlin--Wentzell action functional via large deviation theory. We then reformulate it as a minimization problem in the space of curves through Maupertuis principle. Furthermore we show that the action functionals are intrinsically defined on the manifold. The constrained minimum action method is proposed to compute the minimum action path with the assistance of the constrained optimization scheme. The examples of conformational transition paths for both single and double rod molecules in polymeric fluid are numerically investigated.

Research Area(s)

  • constrained stochastic dynamics, large deviation, optimal transition pathways, rare event

Citation Format(s)

Finding Transition Pathways on Manifolds. / LI, Tiejun; LI, Xiaoguang; ZHOU, Xiang.
In: Multiscale Modeling & Simulation, Vol. 14, No. 1, 2016, p. 173-206.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review